have you looked at the file "class-simplepie.php" in the /wp-includes/ folder?

I'm not familiar with it myself, but it sounds like it has the functionality you seek. i would explore the file to get function names etc and once you've found what you're looking for, go to appearance>editor>header.php and add a require() or include() for the file and update your function calls to the new function names

step one is identifying the deprecated functions that you were trying to use initially. Then identify what they do, hopefully the function names will be descriptive enough to remove a lot of the guesswork there. then browse through the code or documentation for the class-simplepie.php for functions with similar names. in the event that function names in one or both files are less than helpful, you can write up signatures for the deprecated functions; name, input parameters, return value and type. then go through simplepie looking for similar signature. Or you could just google for documentation, but I assumed you had already done